Fig. 3: Mechanistic investigation of Ce³⁺-induced cross-relaxation.

a Emission spectra of the NaYF₄:Yb/Tm@NaYF₄:Ce/Er@NaYF₄ nanoparticles under excitation of 1550 nm at 2073 kW cm⁻² as a function of Ce³⁺ doping concentration in the interlayer. b, c Proposed energy transfer pathways in the NaYF₄:Yb/Tm@NaYF₄:(Ce/)Er@NaYF₄ nanoparticles without and with Ce³⁺ dopants, respectively. d Emission spectra of the NaYF₄@NaYF₄:(Ce/)Er@NaYF₄ nanoparticles without and with Ce³⁺ dopants under 1550 nm excitation at high (2073 kW cm⁻²) and low (5 kW cm⁻²) powers, respectively. e Emission intensity at 346 nm (Tm³⁺) as a function of excitation power density in the NaYF₄:Yb/Tm@NaYF₄:(Ce/)Er@NaYF₄ nanoparticles without and with Ce³⁺ dopants, respectively. f Schematic illustrations of excitation power-dependent preferential population of energy levels in Er³⁺ ions through cross-relaxation with Ce³⁺ dopants. g Simulated populations of ⁴I_11/2 energy levels as a function of excitation power density in NaYF₄:(Ce/)Er without and with Ce³⁺ dopants, respectively. Mechanistic calculations by formulating the rate equations as in the Supplementary Methods.